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          <h1 class="post-title" itemprop="name headline">十大排序算法python实现</h1>
        

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        <ul>
<li>下文中的稳定是指：若a=b，而排序后的ab顺序与原来的ab顺序一样</li>
<li>交换排序：冒泡、快排；<br>选择排序：选择、堆；<br>插入排序：插入、希尔；<br>归并排序、基数排序</li>
<li>总结：</li>
<li>排序算法 | 时间复杂度（平均） | 时间（最短） | 时间（最长） | 空间复杂度 | 是否稳定<br>— | — | — | — | — | —<br>冒泡 | O(N2) | O(N) | O(N2) | O(1) | 是<br>选择 | O(N2) | O(N2) | O(N2) | 0(1) | 否<br>插入 | O(N2) | O(N) | O(N2) | O(1) | 是<br>希尔 | O(n·log(n)2) | O(n3/2) | O(N2) | O(1) | 否<br>快速 | </li>
</ul>
<ol>
<li>冒泡排序</li>
</ol>
<ul>
<li>迭代n-1次，两个相邻元素两两相比，每次迭代将最大的元素放在该迭代序列的顶端。</li>
<li>优化后，对于最优的情况，即已经正序排列的，算法复杂度为O(N)<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">bubble_sort</span><span class="params">(num)</span>:</span></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> range(len(num)<span class="number">-1</span>):</span><br><span class="line">        flag = <span class="number">0</span></span><br><span class="line">        <span class="keyword">for</span> j <span class="keyword">in</span> range(len(num)-i<span class="number">-1</span>):</span><br><span class="line">            <span class="keyword">if</span> num[j] &gt; num[j+<span class="number">1</span>]:</span><br><span class="line">                num[j], num[j+<span class="number">1</span>] = num[j+<span class="number">1</span>], num[j]</span><br><span class="line">                flag = <span class="number">1</span></span><br><span class="line">        <span class="keyword">if</span> flag == <span class="number">0</span>:</span><br><span class="line">            <span class="keyword">return</span> num</span><br><span class="line">    <span class="keyword">return</span> num</span><br></pre></td></tr></table></figure>
</li>
</ul>
<ol start="2">
<li>选择排序</li>
</ol>
<ul>
<li>迭代n-1次，每次选择出最小的放到前面</li>
<li>不稳定，因为选择出最小的之后会跟原有数交换顺序，因此会破坏原来的顺序，例如5 3 5 2，第一次之后为2 3 5 5，此时5跟5的顺序变了</li>
</ul>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">select_sort</span><span class="params">(num)</span>:</span></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> range(len(num)<span class="number">-1</span>):</span><br><span class="line">        min_index = i   </span><br><span class="line">        <span class="keyword">for</span> j <span class="keyword">in</span> range(i,len(num)<span class="number">-1</span>):</span><br><span class="line">            <span class="keyword">if</span> num[j+<span class="number">1</span>] &lt; num[min_index]:</span><br><span class="line">                min_index = j+<span class="number">1</span></span><br><span class="line">        num[i], num[min_index] = num[min_index], num[i]</span><br><span class="line">    <span class="keyword">return</span> num</span><br></pre></td></tr></table></figure>
<ol start="3">
<li>插入排序</li>
</ol>
<ul>
<li>跟打牌类似</li>
<li>最快情况是O(N)，如果大部分数据已经排好序了，while pre_index &gt;= 0 and cur_num &lt; num[pre_index]这句的迭代次数会大大减少，会比较快</li>
</ul>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">insert_sort</span><span class="params">(num)</span>:</span></span><br><span class="line">    <span class="keyword">for</span> i <span class="keyword">in</span> range(len(num)<span class="number">-1</span>):</span><br><span class="line">        pre_index = i <span class="comment"># 前一个数</span></span><br><span class="line">        cur_num = num[i+<span class="number">1</span>] <span class="comment"># 当前待插入数 </span></span><br><span class="line">        <span class="keyword">while</span> pre_index &gt;= <span class="number">0</span> <span class="keyword">and</span> cur_num &lt; num[pre_index]:</span><br><span class="line">            num[pre_index+<span class="number">1</span>] = num[pre_index] <span class="comment"># 往后挪一位</span></span><br><span class="line">            pre_index -= <span class="number">1</span>   </span><br><span class="line">        num[pre_index+<span class="number">1</span>] = cur_num</span><br><span class="line">    <span class="keyword">return</span> num</span><br></pre></td></tr></table></figure>
<ol start="4">
<li>希尔排序</li>
</ol>
<ul>
<li>对插入排序的优化，使用了递减的增量序列</li>
<li>如上所述插入排序中：如果大部分数据已经排好序了，while pre_index &gt;= 0 and cur_num &lt; num[pre_index]这句的迭代次数会大大减少，会比较快 –&gt; 所以希尔排序就是针对这个做了优化，即先减少需要排序的数量，再逐步对其排序</li>
<li>希尔排序是不稳定的算法，它满足稳定算法的定义。对于相同的两个数，可能由于分在不同的组中而导致它们的顺序发生变化。</li>
<li>希尔排序的性能根据其选取的序列而变化</li>
<li>使用动态增量序列的代码如下：</li>
</ul>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">shell_sort</span><span class="params">(num)</span>:</span></span><br><span class="line">    gap = <span class="number">1</span></span><br><span class="line">    <span class="keyword">while</span> gap &lt; len(num) // <span class="number">3</span>: <span class="comment">#gap &lt; (3a,3a+1,3a+2)//3: (a-1)*3+1=3a-2</span></span><br><span class="line">        gap = gap*<span class="number">3</span> + <span class="number">1</span></span><br><span class="line">    <span class="keyword">while</span> gap &gt; <span class="number">0</span>:</span><br><span class="line">        <span class="keyword">for</span> i <span class="keyword">in</span> range(gap,len(num)):</span><br><span class="line">            cur_num = num[gap]</span><br><span class="line">            pre_index = i-gap</span><br><span class="line">            <span class="keyword">while</span> pre_index &gt;= <span class="number">0</span> <span class="keyword">and</span> cur_num &lt; num[pre_index]:</span><br><span class="line">                num[pre_index+gap] = num[pre_index] </span><br><span class="line">                pre_index -= gap</span><br><span class="line">            num[pre_index+gap] = cur_num</span><br><span class="line">        gap //= <span class="number">3</span></span><br></pre></td></tr></table></figure>
<ol start="5">
<li>归并排序</li>
</ol>
<ul>
<li>递归</li>
<li>终止条件：剩一个元素时，返回该元素；再上一层对返回的两个元素比较排序</li>
</ul>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">merge_sort</span><span class="params">(num)</span>:</span></span><br><span class="line">    <span class="function"><span class="keyword">def</span> <span class="title">merge</span><span class="params">(left,right)</span>:</span> <span class="comment"># left和right本身是已经排序好的</span></span><br><span class="line">        result = []</span><br><span class="line">        i=j=<span class="number">0</span></span><br><span class="line">        <span class="keyword">while</span> i &lt; len(left) <span class="keyword">and</span> j &lt; len(right):</span><br><span class="line">            <span class="keyword">if</span> left[i] &lt;= right[j]:</span><br><span class="line">                result.append(left)</span><br><span class="line">                i+=<span class="number">1</span>            </span><br><span class="line">            <span class="keyword">else</span>:</span><br><span class="line">                result.append(right)</span><br><span class="line">                j+=<span class="number">1</span></span><br><span class="line">        result = result + left[i:] + right[j:]</span><br><span class="line">        <span class="keyword">return</span> result</span><br><span class="line"></span><br><span class="line">    <span class="keyword">if</span> len(num) &lt;= <span class="number">1</span>:</span><br><span class="line">        <span class="keyword">return</span> num</span><br><span class="line">    mid = len(num) // <span class="number">2</span></span><br><span class="line">    left = merge_sort(num[:mid])</span><br><span class="line">    right = merge_sort(num[mid:])</span><br><span class="line">    <span class="keyword">return</span> merge(left,right)</span><br></pre></td></tr></table></figure>
<ol start="6">
<li>快速排序</li>
</ol>
<ul>
<li>冒泡+二分+递归分治</li>
<li>核心：每次迭代使选取的基准值插入到序列中，该序列中基准值左边的值小于基准值，右边的值大于基准值，然后再对两边分别迭代</li>
<li>基准数选择以及指针移动顺序：最终两个指针相遇时，要把基准数和相遇的位置交换，此时该位置左边的数小于基准数，右边大于基准数；若选择最左边的数为基准数，肯定要跟比它小的数交换，因此只有右指针先动才能找到比它小的（例如算法2里右指针相遇时找到的一定是上一轮左指针的交换结果，一定是小于基准数的）</li>
</ul>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">## 二分之后不断地递归，每次递归求出基准值的具体位置</span></span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">quick_sort1</span><span class="params">(num)</span>:</span></span><br><span class="line">    <span class="keyword">if</span> len(num) &lt;= <span class="number">1</span>:</span><br><span class="line">        <span class="keyword">return</span> num</span><br><span class="line">    pivot = num[<span class="number">0</span>]</span><br><span class="line">    left = [num[i] <span class="keyword">for</span> i <span class="keyword">in</span> range(<span class="number">1</span>,len(num)) <span class="keyword">if</span> num[i] &lt;= pivot]</span><br><span class="line">    right = [num[i] <span class="keyword">for</span> i <span class="keyword">in</span> range(<span class="number">1</span>,len(num)) <span class="keyword">if</span> num[i] &gt; pivot]</span><br><span class="line">    <span class="keyword">return</span> quick_sort1(left) + pivot + quick_sort2(right)</span><br></pre></td></tr></table></figure>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">quick_sort2</span><span class="params">(num,left,right)</span>:</span></span><br><span class="line">    <span class="keyword">if</span> left &gt;= right: <span class="comment"># 两指针相遇，则终止</span></span><br><span class="line">        <span class="keyword">return</span></span><br><span class="line">    low = left</span><br><span class="line">    high = right</span><br><span class="line">    pivot = num[left]</span><br><span class="line">    <span class="keyword">while</span> left &lt; right:</span><br><span class="line">        <span class="keyword">while</span> left &lt; right <span class="keyword">and</span> num[right] &gt; pivot: <span class="comment"># 右指针向左移动直到找到小于pivot的</span></span><br><span class="line">            right -= <span class="number">1</span></span><br><span class="line">        num[left] = num[right] <span class="comment"># 右边有小于基准值的，调整到左边</span></span><br><span class="line">        <span class="keyword">while</span> left &lt; right <span class="keyword">and</span> num[left] &lt;= pivot: <span class="comment"># 右指针向左移动直到找到小于pivot的</span></span><br><span class="line">            left += <span class="number">1</span></span><br><span class="line">        num[right] = num[left] <span class="comment"># 左边有小于基准值的，调整到右边</span></span><br><span class="line">    num[right] = pivot </span><br><span class="line">    quick_sort2(num, low, left<span class="number">-1</span>)</span><br><span class="line">    quick_sort2(num, right+<span class="number">1</span>, high)</span><br></pre></td></tr></table></figure>
<figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">quick_sort3</span><span class="params">(num,left,right)</span>:</span></span><br><span class="line">    <span class="keyword">if</span> left &lt; right:</span><br><span class="line">        p = partition(num, left, right)</span><br><span class="line">        quick_sort3(num, left, p<span class="number">-1</span>)</span><br><span class="line">        quick_sort3(num, p+<span class="number">1</span>, right)</span><br><span class="line">    </span><br><span class="line"><span class="function"><span class="keyword">def</span> <span class="title">partition</span><span class="params">(num, left, right)</span>:</span></span><br><span class="line">    pivot = num[right] <span class="comment"># 这里是从左边开始移动指针的，因此是right</span></span><br><span class="line">    i = left - <span class="number">1</span></span><br><span class="line">    <span class="keyword">for</span> j <span class="keyword">in</span> range(left, right):</span><br><span class="line">        <span class="keyword">if</span> num[j] &lt;= pivot:</span><br><span class="line">            i += <span class="number">1</span></span><br><span class="line">            num[i], num[j] = num[j], num[i]</span><br><span class="line">    num[i+<span class="number">1</span>], num[right] = num[right], num[i+<span class="number">1</span>] <span class="comment"># 把基准数移过来</span></span><br><span class="line">    <span class="keyword">return</span> i+<span class="number">1</span></span><br></pre></td></tr></table></figure>
      
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